A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
It has been proposed to immerse the substrate in the lithographic projection apparatus in a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the final element of the projection system and the substrate. In an embodiment, the liquid is distilled water, although another liquid can be used. An embodiment of the present invention will be described with reference to liquid. However, another fluid may be suitable, particularly a wetting fluid, an incompressible fluid and/or a fluid with higher refractive index than air, desirably a higher refractive index than water. Fluids excluding gases are particularly desirable. The point of this is to enable imaging of smaller features since the exposure radiation will have a shorter wavelength in the liquid. (The effect of the liquid may also be regarded as increasing the effective numerical aperture (NA) of the system and also increasing the depth of focus.) Other immersion liquids have been proposed, including water with solid particles (e.g. quartz) suspended therein, or a liquid with a nano-particle suspension (e.g. particles with a maximum dimension of up to 10 nm). The suspended particles may or may not have a similar or the same refractive index as the liquid in which they are suspended. Other liquids which may be suitable include a hydrocarbon, such as an aromatic, a fluorohydrocarbon, and/or an aqueous solution.
Most lithographic processes for manufacture of semi-conductor integrated circuits print onto substrates that are circular wafers cut from a single crystal of a semiconductor material, e.g. silicon. Semiconductor devices are generally rectangular in plan and the image field of the lithographic apparatus is also rectangular. Generally, a die is smaller than the image field of a lithographic apparatus however it is possible for the die to be larger than the image field. In that case, multiple exposures are joined by a process known as “stitching”. Therefore, it is a non-trivial problem to optimize the placement of rectangular dies within rectangular image fields so as to maximize the number of good devices that can be manufactured on a wafer. Although the problem is to some extent reduced as wafer sizes increase—300 mm wafers are now standard, 450 mm wafers are proposed—the capital and operating costs of lithographic apparatus are sufficiently high that productivity improvements of even a few percent are worth seeking.
U.S. Pat. No. 6,368,761 discloses a computer-based procedure for maximizing the number of dies that can be produced from a single wafer by consideration of the position of alignment marks and other fixed features of the wafer. A “cost-effectiveness ratio” is used to determine whether or not an exposure that would print only a small number of dies should be carried out.
The article “Optimize Die Size Design to Enhance OWE for Design for Manufacturing” by Chen-Fu Chien et al. (ISSM paper: DM-P-091, 2007) discloses a data mining approach to determining optimum die sizes and/or aspect ratios to achieve a goal of printing as many dies on each wafer as possible and reducing exposure times.
“WAMA—A method of optimizing reticle/die placement to increase litho cell productivity” by A. Dor et al, (Proceedings of SPIE Vol 5756, 2005) discloses a method of maximizing yield by controlling the positioning of dies when using a stepper by referring to a map of the yield potential of every point on the wafer.